To solve for the measure of angle $1$ in the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in any triangle is always $180^\circ$.

We are given:

• One angle is $80^\circ$,
• Another angle is $18^\circ$.

Let $x$ represent the unknown angle (angle 1). Using the Triangle Angle Sum Theorem, we have:

$80^\circ + 18^\circ + x = 180^\circ$

Now, solve for $x$:

$98^\circ + x = 180^\circ$

$x = 180^\circ - 98^\circ$

$x = 82^\circ$

Therefore, the measure of angle 1 is $82^\circ$.

Would you like more details or have any questions? Here are 5 related questions:

1. What is the Triangle Angle Sum Theorem?
2. How would you solve if the triangle were an isosceles triangle?
3. Can you use this theorem for non-Euclidean triangles?
4. How do we solve for angles in quadrilaterals?
5. What are the properties of right-angled triangles?

Tip: Always ensure the sum of the angles in any triangle adds up to $180^\circ$.